This house opened, perhaps as the Princess Theatre, in 1920. This PDF with a brief history of Sweet Springs quotes (on page 19) an article from the March 4 issue of the Sweet Springs Herald:

“C. J. Caldwell has been at work with a force of hands thoroughly remodeling the Hayman property on Lexington Avenue he recently purchased, and fitting it for a modern picture theater. A heating plant was put in, the floor lowered, a balcony built, ticket office, newly decorated and painted, opera chairs have been added, making it one of the nicest and most convenient theaters in this part of the state. The new theater will probably be called ‘The Princess’ and will be in operation within two weeks.”

An item from November, 1931, is also cited, saying that Floyd Ripley had leased the Star Theatre from Mr. Goodnight. The Star Theatre showed its first talking picture on April 15, 1930.

According to the January 14, 1937, issue of The Film Daily this house had been renamed the Mida Theatre: “SWEET SPRINGS— Mida (formerly Star), transferred to D. J. Foley.” But then the March 7 issue listed the Mida in the “Closings” section of its “Theater Changes” column.

The author of the history I cited gives the impression that it was renamed the Ritz Theatre later in 1937, citing an article in the August 13 issue of the Herald:

“The managers of the Ritz Theater are more than pleased with the way their program of up-to-the-minute shows is meeting with public approval. On their opening night, they played to a full house, and their seating capacity has been taxed since then. Miller Brothers, the managers, believe that their cooling system makes the theater the coolest place in town. Next Thursday a new plan is being tried No one will be at the box office selling tickets. but after the show patrons will be given the opportunity of dropping the amount in a box that they think the show was worth.”

Nothing in the document specifically says that the Star became the Ritz. The 1938 FDY actually lists three theaters at Sweet Springs: The Ritz, with 350 seats; the Star, with 400 seats, but closed; and the Uptown, with 394 seats. It’s possible that the FDY just didn’t keep up with the changes and listed the Star/Ritz under both its old and its new name. The Star is not listed in the FDY after 1938. The Ritz is listed through 1945.